Among this plethora of modified gravities let us mention the metric \(f(R)\)  theories , the Metric-Affine (Palatini) \(f(R)\)  gravity [1]}, [2]}, [3]}, the teleparallel \(f(T)\)  gravities [4]}, [5]}, the symmetric teleparallel \(f(Q)\)  [6]}, [7]}, Scalar-Tensor theories [8]}, [9]}, etc and also certain extensions of them (see discussion on chapter \(IV\) ). Of course, the kind of modifications one chooses to adopt is highly a matter of personal taste. In our point of view, interesting and well motivated alternatives are those which extend the underlying geometry of spacetime by allowing a connection more general than the usual Levi-Civita one. In generic settings, when no a priori restriction is imposed on the connection and the latter is regarded as another fundamental field on top of the metric the space will be non-Riemannian [10]} and possesses both torsion and non-metricity. These last geometric quantities can then be computed once the affine connection is found. The theories formulated on this non-Riemannian manifold are known as Metric-Affine theories of gravity [11]}, [12]}.
